Comparative Study On Sample Size Calculation Methods And Implementation By PASS And SAS

Sample size calculation has always been a challenge in medical research. There are more than 90% of medical literatures which didn’t conduct sample size calculation or didn’t do it properly in China, according to statistics. Most researchers have not clearly recognized the importance of sample size calculation, let alone controling over the relevant methods. Consequently, the integrity and validity of their clinical studies are questionable.During the process of determing an appropriate sample size estimation method, researchers will encounter various difficulties such as choosing a proper research design, statistical analysis method, comparison type, accuracy requirement, research time, research funding and so on. Even if these issues have been solved, we still need to go through serious thoughts and careful study on sample size calculation. Using a professional software to calculate sample size has become increasingly popular in the scientific field.In this study, we will guide researchers to find the proper method of sample size calculation efficiently for their research through demonstration of examples using professional softwares, which will help the research more efficient and the results more rigorous, scientific and authentic.Methods of sample size calculation in this study involve:(1)Sample size calculation in estimating the Population mean;(2)Sample size calculation in estimating the Population probability;(3)Sample size calculation in testing for mean of single group design, paired design and crossover design;(4)Sample size calculation in testing the difference of means between two groups;(5)Sample size calculation in testing the equivalence of means between two groups;(6)Sample size calculation in testing the non-inferiority/superiority of means between two groups;(7)Sample size calculation in one-way analysis of variance;(8)Sample size calculation in testing the proportion of single group design;(9)Sample size calculation in testing the difference of proportions between two groups;(10)Sample size calculation in testing the equivalence of proportions between two groups;(11)Sample size calculation in testing the non-inferiority/superiority of proportions between two groups;(12)Sample size calculation in testing two correlated proportions;(13)Sample size calculation in cohort/case-control study;(14)Sample size calculation in correlation analysis;(15)Sample size calculation in testing means for repeated measures design;(16)Sample size calculation in testing means for factorial design;(17) Sample size calculation in survival analysis.Chapter 3 introduces a variety of sample size calculation methods corresponding to common designs starting from the basic formula to the implemention by two professional softwares through examples.Chapter 4-6 introduces sample size calculation methods of several multi-factor designs, including repeated measures design, factorial design and survival analysis. Chapter 7 compares the difference of similar methods in dealing with the same issue.When calculating the sample size of quantitative data of repeated measures design, we divided the methods into two parts, namely, considering only the main effects as well as considering all factors and their interactions. For the first part, the study introduced Bloch’s fomula and Liu K.J’s fomula, and found that it is quite difficult to meet the required prerequisites of Bloch’s method in practice and it is likely to underestimate the sample size. As to the Liu K.J’s method, the required parameters such as conditional correlation coefficient and error of repeated measures are difficult to get.We then calculated the sample size by PASS which not only offers a variety of types of covariance to deal with various situations but also switches parameter values and conditions flexibly. It can accurately and intuitively show the trend and relationship between variables. PASS also provides professional solutions for considering all factors and their interactions. This paper lists the key steps requiring special attention and illustrates them by examples.As to sample size calculaton of factorial design, obtaining the desired parameter estimates from the pilot experiment results is scientific and effective.This study introduces the sample size calculating methods provided by SAS procedure GLMPOWER and PASS which accord to the same principle but require different parameters. GLMPOWER procedure requires mean estimate of each experimental group while PASS requires the mean estimate of each level after combination of the factors.The two methods can both easily obtain the required parameters from the pilot experiment.Afterwards, three types of sample size calculating methods of survival analysis are introduced, including Log-rank tests, group-sequential Log-rank tests and Cox regression.Sample size calculating methods for Log-rank tests mainly include Freedman tests, Lachin-Foulkes tests and Lakatos tests. Freedman’s method is easy but it doesn’t consider the specialty of survival data by assuming fixed hazard proportion, good patient compliance and satisfaction of exponential distribution and so on. More importantly, it doesn’t consider the effect of time factor and censored data, causing the result with large error and can only be used in rough estimate.Lachin-Foulkes’ s method assumes patient entering the study within the time period R, and then do follow-up till the end of time T. It considers censored rate and effect of time.However, the censored rate and hazard proportion in this method are fixed; therefore, it fails to fit the survival process properly. Lakatos’ s method is based on Markov Chains and it considers more uncertain factors. This model can adapt to diversity and complexity of clinical trial well and therefore is a feasible and effective method.As to the sample size estimation of two-group-sequential survivel data, adjustments have to be made to the hypothesis testing procedure to maintain overrall significance and power levels in group-sequential Log-rank tests.This method only considers survival rates in two groups and it can only be used for rough estimate.In terms of sample size calculation of Cox proportional hazards regression model, since there are no special requirement on the distribution of data as long as it fits the Cox proportional hazards assumption, the method is simple, effective and able to take account the influence of single factor as well as covariates.